This invention relates to digital synthesis as an alternative to conventional analog or digital filtering techniques and, more particularly, it relates to a table lookup technique for producing a spectrally shaped, time varying waveform from a sequence of symbol states.
There are a number of drawbacks associated with present implementations of filters. For analog filters, these concerns relate to precision of components, manufacturing reproducibility, lengthy development times and cost of depolyment. For digital filtering, the concerns relate to operational speed and cost of deployment. The real time signal processing used in digital filters typically involves combining weighted versions of a number of temporally spaced signals such as those produced at various taps of a delay line. This weighting is also referred to as the coefficients used in the time domain filtering of digital signals. Such weighting operations are typically performed by digital multipliers. Since digital multiplication is an involved operation, complex circuitry is required to provide the function. The speed limitations of multipliers also renders them economically prohibitive for, or unable to handle the high data rates associated with, the high capacity and the bandlimited transmission of modern communications systems.
In such applications, the demands on filtering must be high in order to provide the desired baseband signals with precise spectral shaping. To meet these demands, analog filters have been traditionally used. However, these analog filters are difficult to design, require time consuming individual tuning during manufacture, are relatively expensive, and are subject to performance deterioration with age or temperature extremes. Moreover, since analog filters are frequency dependent, each time a new system with a different symbol rate or spectral characteristic is used the filters must be completely redesigned. In fact, present symbol rates and modulation techniques are approaching the performance limitations of analog filter technology, which are also at rates beyond the operational speed of conventional digital filter circuit techniques.